Topological band and superconductivity in UTe$_2$

UTe$_2$ has recently been found to be a likely spin-triplet superconductor that exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe$_2$ is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of superconductivity. In particular, we show that DFT+$U$ calculations generically reveal a topological band that originates from a band inversion associated with $5f$ electrons residing on these rung sublattice degrees of freedom. Furthermore, we show that a previously identified strong ferromagnetic interaction within a U-U rung leads to a pseudospin-triplet superconducting state that can account for a non-zero polar Kerr angle, observed magnetic field-temperature phase diagrams, and nodal Weyl fermions. Our analysis may also be relevant for other U-based superconductors.